Achievement standards

Concepts and Techniques

A	B	C	D	E
demonstrates knowledge and understanding of concepts of functions, calculus, vectors and statistics in routine and non-routine problems in a variety of contexts synthesises information to select and apply techniques in mathematics to solve routine and non-routine problems in a variety of contexts develops, selects and applies mathematical models to routine and non-routine problems in a variety of contexts constructs mathematical proofs in a variety of contexts using a range of techniques uses digital technologies effectively to graph, display and organise mathematical information to solve a range of routine and non-routine problems in a variety of contexts	demonstrates knowledge of concepts of functions, calculus, vectors and statistics in routine and non-routine problems synthesises information to select and apply techniques in mathematics to solve routine and non-routine problems selects and applies mathematical models to routine and non-routine problems constructs mathematical proofs in a variety of contexts and adapts previously seen mathematical proofs uses digital technologies appropriately to graph, display and organise mathematical information to solve a range of routine and non-routine problems	demonstrates knowledge of concepts of functions, calculus, vectors and statistics that apply to routine problems selects and applies techniques in mathematics to solve routine problems applies mathematical models to routine problems constructs simple mathematical proofs and adapts previously seen mathematical proofs uses digital technologies to graph, display and organise mathematical information to solve routine problems	demonstrates knowledge of concepts of functions, calculus, vectors and statistics uses simple techniques in mathematics in routine problems demonstrates familiarity with mathematical models reproduces previously seen mathematical proofs uses digital technologies to display some mathematical information in routine problems	demonstrates limited familiarity with simple concepts of functions, calculus, vectors and statistics uses simple techniques in a structured context demonstrates limited familiarity with mathematical models reproduces previously seen simple mathematical proofs uses digital technologies for arithmetic calculations and to display limited mathematical information

Reasoning and Communication

A	B	C	D	E
represents mathematical and statistical information in numerical, graphical and symbolic form in routine and non-routine problems in a variety of contexts communicates succinct and reasoned mathematical and statistical judgments and arguments, including proofs, using appropriate language interprets the solutions to routine and non-routine problems in a variety of contexts explains the reasonableness of the results and solutions to routine and non-routine problems in a variety of contexts identifies and explains the validity and limitations of models used when developing solutions to routine and non-routine problems	represents mathematical and statistical information in numerical, graphical and symbolic form in routine and non-routine problems communicates clear and reasoned mathematical and statistical judgments and arguments, including proofs, using appropriate language interpret the solutions to routine and non-routine problems explains the reasonableness of the results and solutions to routine and non-routine problems identifies and explains limitations of models used when developing solutions to routine problems	represents mathematical and statistical information in numerical, graphical and symbolic form in routine problems communicates mathematical and statistical arguments, including simple proofs, using appropriate language interprets the solutions to routine problems describes the reasonableness of the results and solutions to routine problems identifies limitations of models used when developing solutions to routine problems	represents mathematical and statistical information in numerical, graphical or symbolic form in routine problems communicates mathematical and statistical arguments, including previously seen proofs, using appropriate language describes solutions to routine problems describes the appropriateness of the results of calculations identifies limitations of simple models	represents simple mathematical and statistical information in a structured context communicates simple mathematical and statistical information using appropriate language identifies solutions to routine problems demonstrates limited familiarity with the appropriateness of the results of calculations identifies simple models